Solve y^2-y-2/y^2-3ydivy^2+3y+2/y-3

$$\frac { y ^ { 2 } - y - 2 } { y ^ { 2 } - 3 y } \div \frac { y ^ { 2 } + 3 y + 2 } { y - 3 }$$

Evaluate

$$\frac{y-2}{y\left(y+2\right)}$$

Short Solution Steps

Divide \frac{y^{2}-y-2}{y^{2}-3y} by \frac{y^{2}+3y+2}{y-3} by multiplying \frac{y^{2}-y-2}{y^{2}-3y} by the reciprocal of \frac{y^{2}+3y+2}{y-3}.

$$\frac{\left(y^{2}-y-2\right)\left(y-3\right)}{\left(y^{2}-3y\right)\left(y^{2}+3y+2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-3\right)\left(y-2\right)\left(y+1\right)}{y\left(y-3\right)\left(y+1\right)\left(y+2\right)}$$

Cancel out \left(y-3\right)\left(y+1\right) in both numerator and denominator.

$$\frac{y-2}{y\left(y+2\right)}$$

Expand the expression.

$$\frac{y-2}{y^{2}+2y}$$

Expand

$$\frac{y-2}{y\left(y+2\right)}$$

Short Solution Steps

Divide \frac{y^{2}-y-2}{y^{2}-3y} by \frac{y^{2}+3y+2}{y-3} by multiplying \frac{y^{2}-y-2}{y^{2}-3y} by the reciprocal of \frac{y^{2}+3y+2}{y-3}.

$$\frac{\left(y^{2}-y-2\right)\left(y-3\right)}{\left(y^{2}-3y\right)\left(y^{2}+3y+2\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(y-3\right)\left(y-2\right)\left(y+1\right)}{y\left(y-3\right)\left(y+1\right)\left(y+2\right)}$$

Cancel out \left(y-3\right)\left(y+1\right) in both numerator and denominator.

$$\frac{y-2}{y\left(y+2\right)}$$

Expand the expression.

$$\frac{y-2}{y^{2}+2y}$$